Viracocha,
I bought a motorbike from Banbury earlier this year, and I promise you , the nearest steep hill is the Cotswolds, over five miles away from the market square.
While we were there, we has lunch in the Fine Lady restaurant, attached to the Banbury Cross pub.
The Bike, by wonderful coincidence, has the reg letters LDY. - and is called Lady, of course.
I do recall a radio broadcast which insists that the rhyme should refer to Coventry Cross, and is about Lady Godiva- which is the presumed excuse for the pictures of naked fine ladies on view in Banbury,
Cheers
Dave